On-site correlations in optical lattices: band mixing to coupled quantum Hall puddles

TL;DR

This paper extends the Bose-Hubbard model to include strong on-site correlations, crucial for accurate experimental modeling and understanding exotic states like quantum Hall puddles, affecting phase diagrams and condensate properties.

Contribution

The authors develop a generalized Bose-Hubbard model that captures arbitrarily strong on-site correlations, including effects relevant for Feshbach resonances and rotating lattices.

Findings

On-site correlations significantly alter the phase diagram.

Mean field approximation captures all on-site correlations.

Correlations lead to condensate depletion.

Abstract

We extend the standard Bose-Hubbard model to capture arbitrarily strong on-site correlations. In addition to being important for quantitatively modeling experiments, for example, with Rubidium atoms, these correlations must be included to describe more exotic situations. Two such examples are when the interactions are made large via a Feshbach resonance, or when each site rotates rapidly, making a coupled array of quantum Hall puddles. Remarkably, even the mean field approximation to our model includes all on-site correlations. We describe how these on-site correlations manifest themselves in the system's global properties: modifying the phase diagram and depleting the condensate.